Estimation of optimal PDE-based denoising in the SNR sense

Guy Gilboa*, Nir Sochen, Yehoshua Y. Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


This paper is concerned with finding the best partial differential equation-based denoising process, out of a set of possible ones. We focus on either finding the proper weight of the fidelity term in the energy minimization formulation or on determining the optimal stopping time of a nonlinear diffusion process. A necessary condition for achieving maximal SNR is stated, based on the covariance of the noise and the residual part. We provide two practical alternatives for estimating this condition by observing that the filtering of the image and the noise can be approximated by a decoupling technique, with respect to the weight or time parameters. Our automatic algorithm obtains quite accurate results on a variety of synthetic and natural images, including piecewise smooth and textured ones. We assume that the statistics of the noise were previously estimated. No a priori knowledge regarding the characteristics of the clean image is required. A theoretical analysis is carried out, where several SNR performance bounds are established for the optimal strategy and for a widely used method, wherein the variance of the residual part equals the variance of the noise.

Original languageEnglish
Pages (from-to)2269-2280
Number of pages12
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - Aug 2006


FundersFunder number
Adams Center
EC 6th Framework IST Programme
Israeli Ministry of Science
Ollendorf Minerva Center
Tel-Aviv University fund
National Science FoundationDMS-0312222, ITR ACI-0321917
National Institutes of Health
National Institute of Mental HealthP20MH065166
European Commission
Israel Science Foundation
Technion-Israel Institute of TechnologyHPRN-CT-2002-00285


    • Image denoising
    • Nonlinear diffusion
    • Signal-to-noise ratio (SNR)
    • Total-variation
    • Variational image processing


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